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If a, b, and c are not equal to zero, what is the difference between the maximum and minimum value of S? S = 1 + 
- a)12
- b)14
- c)22
- d)20
- e)18
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
If a, b, and c are not equal to zero, what is the difference between t...
Understanding Absolute Values
= 1 When a is positive.
= 1 When a is negative.
Step 1: Compute the Maximum Value of S
When will the value of the expression be maximum?
The value of the expression will be maximum when all of the terms become positive.
i.e., a, b, and ab should be positive and c should be negative.
When a is positive,
When b is positive,
When a and b are positive, as required in the previous two steps, ab will be positive and the expression,
When c is negative,
Therefore, the maximum value = 1 + 1 + 2 + 3 -(-4) = 11
Step 2: Compute the Minimum Value of S
When will the value of the expression be minimum?
= 1 When a is positive.= 1 When a is negative.Step 1: Compute the Maximum Value of S
When will the value of the expression be maximum?
The value of the expression will be maximum when all of the terms become positive.
i.e., a, b, and ab should be positive and c should be negative.
When a is positive,
When b is positive,
When a and b are positive, as required in the previous two steps, ab will be positive and the expression,
When c is negative,
Therefore, the maximum value = 1 + 1 + 2 + 3 -(-4) = 11
Step 2: Compute the Minimum Value of S
When will the value of the expression be minimum?
The value of the expression will be minimum if we make as many terms negative as possible.
Higher the magnitude of the terms made negative, lower the value of the expression.
c has to be positive for S to be minimum. The last term will then be -4.
If ab is negative, then
If ab has to be negative, one of a or b has to be positive and the other has to be negative.
Possibility 1: If a > 0 and b < 0,
The value of the expression is 1 + 1 - 2 - 3 - 4 = -7.
Possibility 2: If a < 0 and b > 0,
The value of the expression is 1 - 1 + 2 - 3 - 4 = -5.
Therefore, the minimum value is -7
Step 3: Compute the difference
Maximum value of S = 11.
Minimum value of S = -7.
The difference is 18.
Choice E is the correct answer.
Higher the magnitude of the terms made negative, lower the value of the expression.
c has to be positive for S to be minimum. The last term will then be -4.
If ab is negative, then
If ab has to be negative, one of a or b has to be positive and the other has to be negative.
Possibility 1: If a > 0 and b < 0,
The value of the expression is 1 + 1 - 2 - 3 - 4 = -7.
Possibility 2: If a < 0 and b > 0,
The value of the expression is 1 - 1 + 2 - 3 - 4 = -5.
Therefore, the minimum value is -7
Step 3: Compute the difference
Maximum value of S = 11.
Minimum value of S = -7.
The difference is 18.
Choice E is the correct answer.
Most Upvoted Answer
If a, b, and c are not equal to zero, what is the difference between t...
Understanding Absolute Values
= 1 When a is positive.
= 1 When a is negative.
Step 1: Compute the Maximum Value of S
When will the value of the expression be maximum?
The value of the expression will be maximum when all of the terms become positive.
i.e., a, b, and ab should be positive and c should be negative.
When a is positive,
When b is positive,
When a and b are positive, as required in the previous two steps, ab will be positive and the expression,
When c is negative,
Therefore, the maximum value = 1 + 1 + 2 + 3 -(-4) = 11
Step 2: Compute the Minimum Value of S
When will the value of the expression be minimum?
= 1 When a is positive.= 1 When a is negative.Step 1: Compute the Maximum Value of S
When will the value of the expression be maximum?
The value of the expression will be maximum when all of the terms become positive.
i.e., a, b, and ab should be positive and c should be negative.
When a is positive,
When b is positive,
When a and b are positive, as required in the previous two steps, ab will be positive and the expression,
When c is negative,
Therefore, the maximum value = 1 + 1 + 2 + 3 -(-4) = 11
Step 2: Compute the Minimum Value of S
When will the value of the expression be minimum?
The value of the expression will be minimum if we make as many terms negative as possible.
Higher the magnitude of the terms made negative, lower the value of the expression.
c has to be positive for S to be minimum. The last term will then be -4.
If ab is negative, then
If ab has to be negative, one of a or b has to be positive and the other has to be negative.
Possibility 1: If a > 0 and b < 0,
The value of the expression is 1 + 1 - 2 - 3 - 4 = -7.
Possibility 2: If a < 0 and b > 0,
The value of the expression is 1 - 1 + 2 - 3 - 4 = -5.
Therefore, the minimum value is -7
Step 3: Compute the difference
Maximum value of S = 11.
Minimum value of S = -7.
The difference is 18.
Choice E is the correct answer.
Higher the magnitude of the terms made negative, lower the value of the expression.
c has to be positive for S to be minimum. The last term will then be -4.
If ab is negative, then
If ab has to be negative, one of a or b has to be positive and the other has to be negative.
Possibility 1: If a > 0 and b < 0,
The value of the expression is 1 + 1 - 2 - 3 - 4 = -7.
Possibility 2: If a < 0 and b > 0,
The value of the expression is 1 - 1 + 2 - 3 - 4 = -5.
Therefore, the minimum value is -7
Step 3: Compute the difference
Maximum value of S = 11.
Minimum value of S = -7.
The difference is 18.
Choice E is the correct answer.
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